Method of correcting an arcuate track



A ril 18, 1967 F. PLASSER ETAL 3,314,154

Filed NOV 9, 1965 INVENTORS.

PM: PLnssER, TobEF "rnmnel 61m scnuan'r'r Aaewr Filed Nov. 9, 1965 April 18, 1967 F. PLAssER ETAOL I 3,314,154

METHOD OF CORRECTING AN ARCUATE TRACK 25 Sheets-Sheet.2

INVENTORS'. FRAML pLn-ss April 18, 1967 F. PLASSER ETAL 3,314,154

METHOD OF CORRECTING AN ARGUATE TRACK Filed Nov. 9, 1965 5 Sheets-Sheet 5 United States Patent METHOD OF CORRECTING AN ARCUATE TRACK Franz Plasser and Josef Theurer, both of Johannesgasse 3, and Egon Schubert, Sturzgasse 17, all of Vienna,

Austria Filed Nov. 9, 1965, Ser. No. 511,282 Claims priority, application Austria, Nov. 13, 1964, A 9,644/64 Claims. (Cl. 33-1) This application is a continuation-in-part of our copending application Ser. No. 444,556, filed Apr. 1, 1965, now abandoned, which is a continuationinapart of our application Ser. No. 32,904, filed May 31, 1960, now abandoned.

The invention relates to a method of correcting the position of railroad tracks and the like, and particularly to a method of correcting the position of tracks originally built to extend in a circular arc or other arcuate shape of precisely definable geometric shape, and displaced from the original or nominal position during use.

The invention is based on the known geometrical relationships between a long chord drawn to the ends of an are, a short chord drawn between any two points of the arc, and a straight line drawn from the long chord on the are and intersecting the short chord. The two sections of the line on either side of the point of intersection with the short chord are related in a manner which is known or readily calculated if the length of the two chords or equivalent quantitative data, and one other parameter relating to the relative position of the chords are known.

In applying these geometrical relationships to the problem of correcting the position of a track, further use also is made of the fact that the deviation of a set of remote points of the track from a relative position corresponding to the nominal circular shape of the track is normally smaller than the deviation of a set of points closely spaced when a correction is made for the diiferent distances between the two points of the two sets. Differently worded, the distance of an end point of a long chord drawn on an uncorrected track section from its corrected position, when divided by the length of the chord, is normally smaller than the corresponding distance of an end point of a shorter chord drawn on the same track section, when divided by the length of the shorter chord. Useful results may therefore be obtained in making short-range track corrections by assuming that the overall shape of the uncorrected track conforms to the design shape. The corrections made on the basis of the last-mentioned assumption may not restore the track section to a precisely circular shape, but they cause the track section to approach the circular shape more closely than prior to correction. If the results obtained in a first correction are not satisfactory, the procedure may be repeated as often as needed, thereby moving the track closer to the desired shape in each correction, and approaching the predetermined shape to any degree desired. A single correction procedure is usually adequate, and more than two are seldom needed.

A salient feature of the invention is the use of a previously corrected track section or of a track section assumed to have the correct shape as a basis for measurements from which data for track correction are derived. Typically, such data are obtained from a set of measurements or observations taken on corrected track and on one, or at most two readings taken in part on an uncorrected portion of the track, and carefully chosen so as not unduly to affect the accuracy of the results.

j In its more specific aspects, the invention contemplates the sequential correction of track sections which partly overlap each other so that each track section has a portion in common with a previously corrected preceding portion,

Two chords are drawn from this common portion of the track section to be corrected to that portion which is not common. The first chord extends between the ends of the section, and the second chord is shorter than the first. The second chord is laid in a fixed geometrical relationship to the first chord, and this relationship may be of many kinds, as will presently become apparent.

A straight line is drawn from the first chord in a predetermined direction toward the portion of the track section common with a preceding section, and previously corrected. The line intersects the second chord in such a manner that the point of intersection divides the line into two parts. The part of the track section on which the uncorrected end of the second chord is located is then shifted in such a direction that the relationship of the two parts of the intersected straight line approaches the relationship of corresponding line parts in an are having the desired shape.

In carrying out the invention, we may use small vehicles that can travel on the track and are connected in pairs by rigid rods or tension members for laying the chords or for establishing reference points. The line intersecting the shorter chord and connecting the longer chord to the track section may be drawn by means of measuring tape or in any other desired manner. The shifting of the track at an end point of the shorter chord is performed by means of well known track-aligning equipment commonly referred to as track lining machines and not requir-ing more detailed description.

The exact nature of this invention as well as other features and advantages thereof will be readily apparent from consideration of the following specification relating to the annexed drawing in which:

FIG. 1 illustrates the geometrical relationships in a circle relevant to a first embodiment of the invention;

FIG. 2 illustrates geometrical relationships relevant to a modification of the method based on FIG. 1;

FIG. 3 shows a geometrical relationship in a circle underlying yet another embodiment of this invention;

FIG. 4 illustrates yet another modified method of correcting the position of a circular track in the manner of FIGS. 1 to 3;

FIG. 5 shows the application of the method of the invention to a track having the nominal shape of a parabolic spiral;

: FIG. 6 illustrates certain relationships in a cubical parabola which are being utilized in the method of the invention; and

FIG. 7 shows a variation of the method of FIG. 6.

Referring now to the drawing in detail, and initially to FIG. 1, there is seen a circular are 10 whose end points 1, 2 are connected by a chord 3. A line 4 perpendicular to the chord 3 is drawn from the mid-point 5 of the chord 3 to the mid-point 6 of the are 10. A second chord 7, parallel to the chord 3 and of known length, is laid between two points 8 and 9 of the arc Ill which are spaced from the points 1, 2 respectively toward the mid-point 6. The second chord intersects the line 4 in the point 11, and divides the line into two portions 12 and 13, portion 12 extending between the two chords.

If the length of the second chord 7 is s, the length of the first chord 3 is n x s, the length of the line 4 is F, and the length of the line portion 13 is i, then it is known for arcs whose radius is much. greater than the cord 3 that We place two vehicles connected by rigid rods or tension members, such as a cable or chain, at two relatively widely spaced points of the track so that they are located at the end points of a curved track section to be corrected. The known length of the connecting rods or of the tensioned chain or cable provides knowledge of the length of the chord between the two points.

A second pair of vehicles connected by shorter rods, chains, or cables of known length is then placed on the track between the first pair in such a manner that the rods, chains, or cables connecting the two pairs are parallel. A line is next drawn perpendicularly from the mid point of the chord between the first pair of vehicles on the track, and the length of the two ortions of the line on either side of its intersection with the second chord are measured. If the relationship of the line portion does not satisfy Equation I, the track is shifted at either or both vehicles of the second pair until the two sections of the line satisfy the known relationship for a circular arc while maintaining the lengths and the parallel alignment of the chords defined by the two pairs of vehicles.

Both pairs of vehicles may then be moved along the track until another track section is bounded by the first pair of vehicles, and the procedure is repeated. The second track section overlaps the first section so that eventually a condition is reached in which one vehicle of each pair and the point 6 are located on a corrected track portion, and the results obtained under such a condition so closely approximate a circular lay-out of the corrected track that a secondary correction repeating the same procedure on the same track section is often unnecessary.

It will be obvious to those skilled in the art, that the relationship between the portions 12, 13 of the line 4 to the lengths of the chords 3, 7 need not be measured directly, but may be derived from measurements of angles in the manner illustrated in FIG. 2.

FIG. 2 shows the circular are 10, chords 3, 7, and line 4 correlated in the same manner as in FIG. 1. Lines of sight drawn from the point 6 to the end points 1, 8 of the chords 3, 7 respectively define angles a, B with the chords.

The following relationships are evident from FIG. 2:

'i LLZIL JL LI tan oz s 2F F n (III) It is apparent from Equation III that it is not necessary actually to measure the line 4, but that adjustment of the track at the end points of the second chord represented by the second pair of vehicles may be made until the lines of sight drawn from the midpoint 6 of the are on the vehicles of the two pairs enclose angles with the two chords whose tangent values are related to each other as the lengths of the two chords. If this relationship of the angles is reached, the portions of the line 4 inherently are related to the lengths of the chords as described hereinabove with respect to FIG. 1.

Other known geometrical relationships between a longer chord, a shorter chord, and a line drawn from the longer chord on a circular arc and intersecting the shorter chord may be used in correcting a curved track according to this invention, and such a different relationship is illustrated in FIG. 3.

The are 10 is bounded by a chord 3 as in FIGS. 1 and 2, and it will be assumed that the chord 3 is much shorter than the radius of the are 10, a condition inherently fulfilled in the correction of railroad tracks, as normally practiced. A line 14 is drawn to the arc 10 from a point 15 on the chord 3 which divides the chord 3 in a ratio of 1:3, and meets the are 10 at a point 16. A cord 17 is drawn from the end 1 of the chord 3 to the midpoint 6 of the are 10. It intersects the line 14 in the point 18 in such a manner that the portion 19 of the line between the points 16 and 18 is one third of the entire line 14 between the points 15 and 16.

In making use of this relationship in the correcting of a curved track toward its nominal circular configuration, we place two vehicles relatively remotely apart on the ends of a track section, so that a first set of rods, chains, or cables connecting the vehicle defines a chord corresponding to the chord 3 in FIG. 3.

A third vehicle is connected to one of the aforementioned vehicles by a second set of rods, cables, or chains long enough to place the vehicle at the midpoint of the are, thereby defining a shorter chord corresponding to the chord 17 in FIG. 3. A line is then drawn at right angles from the three-quarters point of the first set of connecting members between the first-mentioned two vehicles to intersect the chord defined by the third vehicle and the second set of connecting members attached thereto, and the position of the last-mentioned vehicle, approximately corresponding to the point 6 in FIG. 3 is shifted until the two portions of the line defined by intersection with the afore-mentioned second set are related as required, that is, at a ratio of one to two.

The relevant fixed geometrical relationship of the two chords 3 and 17 in FIG. 3 is the fact that they have one end point in common. The corresponding relationship of the chords 3 and 7 in FIGS. 1 and 2 is their parallel alignment. Obviously, many other fixed relationships between a longer chord connecting the ends of a circular arc, a shorter chord conecting any two points of the arc, and a line extending from the longer chord to the arc and intersecting the shorter chord may be utilized in carrying out the method of the instant invention. Some such additional relationships are known, and others may be developed readily from the foregoing teachings.

Yet another modification of the method of the invention is illustrated in FIG. 4 in which an are 10 represents a track section of nominally circular configuration which was partly corrected by one of the methods described hereinabove, the corrected portion extending from a point 1 slightly beyond 6 but ending short of the point 9.

In correcting the track position at or near the point 9, a conventional track lining machine is positioned at that point. Rigid rods, indicated in the drawing by broken lines, hingedly connect the track lining machine with four small vehicles capable of traveling on the track. The two rods connecting the vehicles at the end points 1, 2 of the track with the vehicle at point 8 and the track lining machine at point 9 are of equal known length a. The chords 1-2 and 8-9 defined by the end points of these rods thus are nominally parallel. The two rods connecting the vhicle at point 6' with the vehicle at 8 and the track lining machine dififer in length, so that their length may be expressed as 19-}- c and b- 0, respectively. Typically, a is chosen to be 20 ft., b also may be 20 ft., and 0 one foot. Chords are laid out between point 1, 2 and 8, 9 by stretched ropes, and the perpendicular distances from the vehicle at 6 to the chord 8-9 at 11 and to the chord 12 are measured along the line 4.

If the distance 6'11 is f, and the entire length of the line 4' is F, the ratio f/F in a circle should satisfy the relationship if b=a2 and should have a value of 1/4.01 when a and c have the numerical values indicated above.

If f is found to be smaller than determined by the required ratio, the track is shifted laterally inward of the are by the track lining machine at point 9 until the point of intersection 11 is properly located. The track lining machine is then shifted with its satellite vehicles toward the point 2, and the operation described above is repeated.

In the afore-described track aligning operation, the vehicles at points 1, 8, 6' stand on previously aligned track, and the error in the position of the vehicle at 2 has only a minor effect on the position of the rope which oonmeets the vehicles at 1 and 2. because of the relatively large distance of these points. The correction in the track position at point 9 is thus based on the positions of previously corrected points or on the position of track points whose deviation from a corrected position does not materially affect the result.

The method of the invention may readily be modified for application to track sections which are not nominally circular arcs but whose radius of curvature varies, as in parabolic or other non-circular arcs. Track sections of such varying curvature are employed for connecting two circularly arcuate sections of different radii of curvature, or one circular section with a straight section and such track sections will be referred to hereinafter as transitional track sections. FIG. 5 shows relevant geometrical relationships in a track section which is nominally defined by a parabolic spiral.

A track lining machine is placed on the track section at the point 22, and is hingedly connected with four satellite vehicles by rigid rods having equal length of 20 ft. and not themselves indicated in the drawing. Two vehicles are respectively positioned at points 20, 21 behind the machine and two at points 23, 24 ahead of the ma chine.

A rope or wire is tensioned between the outermost vehicles to lay a chord 20-24. A second chord is laid from the point 20 through a point 25 which is spaced from the machine at 22 toward the chord 20-24. The spacing v, in inches, for a rod length of 20 ft. is calculated from the formula wherein K is the degree of curve, and L is the length of the transitional track section in feet. The value of 11/2 is proportional to the cube of the rod length. For 30 ft. long rods, the above quation would assume the values ;1 1.s0K t 2 L t An ordinate is laid from the point 21, equidistant from points 20, 22 to the chord 20-24 at 26. The distance F i is measured between points 21 and 26, and the distance proper relationship is established. Conversely, an excessive value of f is corrected by shifting the track at 22 outward of the arc.

After performing the track correction at 22, the track lining machine is moved in a direction from 20 toward 24 a suflicient distance, say ten feet, to prevent the previously corrected track section at 22 from being disturbed when the cycle of measurements and corrections is repeated with the track lining machine at its new location. Care must be taken, however, to position the vehicles arranged behind the track lining machine on track portions which were previously corrected.

The value of v/2 is Zero for tracks conforming to circular arcs, and for arcs whose radius of curvature is infinite, that is, straight track sections.

A method of correcting the position of a transitional track section basically similar to the methods described hereinabove, but simple and capable of being automatized in an obvious manner, is illustrated in FIG. 6. The track section to be corrected has the nominal shape of a cubical parabola and extends from a starting point 30 to or beyond a point 24.

A track lining machine is positioned on the track at a point 22 and is connected to satellite vehicles on the track, at points 20, 21, 23, 24 by interposed hinged, rigid rods of equal length. The vehicles at 20, 24 thus define a long chord and are connected by a rope or the like along the chord. A short chord connects the machine at 22 with the vehicle at 20, and ordinates at right angles to the chord 20-24 are laid to points 26, 28 respectively on the long chord from points 21 and 23, respectively. The short chord 20-22 intersects the ordinate 21-26 at 27 The distances 20-21, 21-22, 22-23 and 23-24, are equal and are represented in the following equations by a. The length of the ordinate 21-26 shall be P, and that of the ordinate 23-28 shall be G. The distance of the point 30 from the first satellite vehicle at 20 shall be d, and the length of the ordinate portion 27-21 shall be f. If the total length of the parabola is L, and its radius is R, the following relationships are known to hold:

The assumption that :F =1:3 by analogy to FIG. 3 is, therefore, erroneous by a factor of It is further evident from the afore-cited known relationships that It follows that the track at 22 must be shifted by the track lining machine until the distance 21-27 is equal to F/ 3 minus /3 (G-F), or until a chord drawn through the point 20 and a point 25 intersects the ordinate F at 27 so as to divide the chord into two portions of which one has twice the length of the other. The point 25 lies on an ordinate drawn through the point 22, and the distance 22-25 is equal to /3 (G-F).

It will be appreciated that a minor element of inaccuracy is introduced into the correction method of FIG. 6 by employing a measurement taken on a point 23 which is on a track portion not previously corrected, but the error introduced has been found to be insignificant. The method described with reference to FIG. 6 is readily automatized by the use of mechanical, electrical, or electronic devices for measuring the distances F, f and G.

A different approach to the same solution for correcting a parabolic track is illustrated in FllG. 7 in which the starting point of the transition, the positions of a track lining machine at 22 and of its satellite vehicles at 20, 21, 23, 24 are related as described above. An ordinate drawn from point 21 to the long chord 20-24 is intersected at 27 by a chord connecting the points 20, 22, and a chord connecting the points 22, 24 similarly intersects at 29 and an ordinate drawn from the point 23 to the long chord 20-24.

It will be appreciated that the radii of curvature in FIG. 7, as in the other figures of the drawing, have been reduced in length for greater clarity of pictorial representation, as compared to the spacings between the track lining machine 22 and its satellite vehicles at 20, 21, 23, 24. The angles 7 and 5, defined by the bars which connect the vehicles at 21 and 23 to the track lining machine 7 at 22, and by the chords 20-22 and 22-24, are therefore so small that it may validly be assumed that tan 'y f/a tan 5=g/a wherein f and a have the same meaning as in FIG. 5,

The correction required in the assumption that F :3 f, as determined in the description of FIG. 6, is therefore The correction factor is thus readily determined from measurement of the angles 'y and 5 which is capable of being performed automatically by mechanical or electronic equipment. The results obtained may be directly fed to a computer for controlling the lateral shifting of the track by the track lining machine at 22.

It should be understood, of course, that the foregoing disclosure relates only to preferred embodiments of the invention, and that it is intended to cover all changes and modifications of the examples of the invention herein chosen for the purpose of the disclosure which do not constitute departures from the spirit and scope of the invention set forth in the appended claims.

What we claim is:

1. A method of correcting a track having a first portion substantially conforming to a predetermined arcuate shape and a second portion deviating from said shape which comprises:

(a) sequentially laying respective first chords between the ends of a plurality of sections of said track, said sections overlapping each other, and the ends of each first chord being respectively located in said first and second portions;

(b) sequentially laying a second chord shorter than the corresponding first chord between a pair of points of each track section in a fixed geometrical relationship to said corresponding first chord, one of said points being located in said first track portion, and the other point being located in said second portion and spaced from said ends of the associated track section;

(c) laying a straight line in a predetermined direction from each first chord to the associated track section in said first portion of said track, each line intersecting the corresponding second chord in such a manner that the point of intersection divides the line into two parts; and

((1) moving said other point of each track section while maintaining said fixed geometrical relationship of said first and second chords until the relationship of the lengths of said two parts of the corresponding line and of said chords corresponds to the relationship of corresponding line parts and chords in an arc of said predetermined shape.

2. A method as set forth in claim 1, wherein said predetermined shape is circular, said first chords are of substantially equal length, and said second chords are of substantially equal length.

3. A method of correcting a track approximately corresponding to a predetermined arcuate shape toward more precise conformity with said shape which comprises:

(a) sequentially laying respective first chords between the ends of a first and of a second section of said track, said sections overlapping each other, whereby a portion of said track is common to said sections;

(b) sequentially laying respective second chords shorter than said first chords between two end points on said track sections in a fixed geometrical relationship to the corresponding first chords, one of the end points of the second chord associated with said second section being located on said common portion, and the other end point of said second chord of the second section being spaced from said first track section;

(0) laying a straight line in a predetermined direction from each first chord to the associated track section, each line intersecting the corresponding second chord in such a manner that the point of intersection divides the line into two parts, and the line laid to said second track section from the corresponding first chord meeting said common portion; and

(d) sequentially moving the parts of the track on which the other end points of said second chords are located in such a direction that the relationship of the lengths of said two parts of the respective lines to each other approaches the relationship of corresponding line parts in an are having said predetermined shape.

4. A method as set forth in claim 3, wherein said straight line from the first chord of said track section is laid to said common portion after said moving of the part of the track on which the other end point of the second chord of said first section is located.

5. A method as set forth in claim 4, wherein said straight line is perpendicular to the associated first chord.

6. A method as set forth in claim 4, wherein said first chords are parallel to the associated chords.

7. A method as set forth in claim 4, wherein one end of each first chord coincides with one end point of the associated second point, the coinciding end and end point associated with said second track section being located on said common portion.

8. A method as set forth in claim 4, wherein said straight line is perpendicular to the associated first chord and bisects the associated track section.

9. A method as set forth in claim 4, wherein said predetermined shape is circular,

10. A method as set forth in claim 4, wherein said predetermined shape is parabolic.

References Cited by the Examiner UNITED STATES PATENTS 1,127,204 2/ 1915 Bobyns 331 2,531,461 11/1950 Petry 336O FOREIGN PATENTS 326,942 10/1920 Germany.

LEONARD FORMAN, Primary Examiner.

S. S. MATTHEWS, Assistant Examiner.

c. P. Allen,

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3,314,154 April 18, 1967 Franz Plasser et a1.

certified that error appears in the above numbered pat- It is hereby hat the said Letters Patent should read as ent requiring correction and t corrected below.

In the heading to the printed specification, line 7, after "Austria," insert May 29, 1959, A 3986/59;

Signed and sealed this 21st day of January 1969.

(SEAL) Attest:

EDWARD J. BRENNER Commissioner of Patents Edward M. Fletcher, Jr.

Attesting Officer 

1. A METHOD OF CORRECTING A TRACK HAVING A FIRST PORTION SUBSTANTIALLY CONFORMING TO A PREDETERMINED ARCUATE SHAPE AND A SECOND PORTION DEVIATING FROM SAID SHAPE WHICH COMPRISES: (A) SEQUENTIALLY LAYING RESPECTIVE FIRST CHORDS BETWEEN THE ENDS OF A PLURALITY OF SECTIONS OF SAID TRACK, SAID SECTIONS OVERLAPPING EACH OTHER, AND THE ENDS OF EACH FIRST CHORD BEING RESPECTIVELY LOCATED IN SAID FIRST AND SECOND PORTIONS; (B) SEQUENTIALLY LAYING A SECOND CHORD SHORTER THAN THE CORRESPONDING FIRST CHORD BETWEEN A PAIR OF POINTS OF EACH TRACK SECTION IN A FIXED GEOMETRICAL RELATIONSHIP TO SAID CORRESPONDING FIRST CHORD, ONE OF SAID POINTS BEING LOCATED IN SAID FIRST TRACK PORTION, AND THE OTHER POINT BEING LOCATED IN SAID SECOND PORTION AND SPACED FROM SAID ENDS OF THE ASSOCIATED TRACK SECTION; (C) LAYING A STRAIGHT LINE IN A PREDETERMINED DIRECTION FROM EACH FIRST CHORD TO THE ASSOCIATED TRACK SECTION IN SAID FIRST PORTION OF SAID TRACK, EACH LINE INTERSECTING THE CORRESPONDING SECOND CHORD IN SUCH A MANNER THAT THE POINT OF INTERSECTION DIVIDES THE LINE INTO TWO PARTS; AND (D) MOVING SAID OTHER POINT OF EACH TRACK SECTION WHILE MAINTAINING SAID FIXED GEOMETRICAL RELATIONSHIP OF SAID FIRST AND SECOND CHORDS UNTIL THE RELATIONSHIP OF THE LENGTHS OF SAID TWO PARTS OF THE CORRESPONDING LINE AND OF SAID CHORDS CORRESPONDS TO THE RELATIONSHIP OF CORRESPONDING LINE PARTS AND CHORDS IN AN ARC OF SAID PREDETERMINED SHAPE. 